Listen to Robert Emmerich introduce The Big Apple, a hit song from 1937. Music written by Bob and performed by Tommy Dorsey's Clambake Seven with Bob on piano. Lyrics written by Buddy Bernier and sung by Edythe Wright. Audio provided by Dorothy Emmerich.

To be cast in a Hollywood or a Broadway production, the old saying is that a starlet sleeps with the director to get the part. “She’s so dumb/stupid, she slept with the writer” is a jocular saying illustrating the lowly place of a writer in a production, especially on a Hollywood set.

“One of the oldest inside jokes out there is of the starlet so dumb she slept with the screenwriter in hopes of advancing her career” was cited in print in 1986, but the joke is probably much older.

Google News Archive
8 June 1988, Glasgow (Scotland) Herald, “Hollywood strifes” by Anne Simpson, pg. 12, col. 7:
And, indeed, if anyone has a real cause for revenge in Hollywood it is the creatively fleeced, and often uncredited, scenarists who for years have been labouring under that cheap, humiliating barb about the movie starlet who was so dumb she slept with a screenwriter.

New York (NY) TimesAnatomy of a Sitcom
By Linda Blandford: Linda Blandford writes from Los Angeles for The Guardian of London
Published: April 02, 1989
(...)
Writers, as everyone knows, are the lackeys of the film industry. (The starlet joke goes: “She was so dumb, she slept with the writer.") The exception is situation comedy. They call it ‘’the voice,’’ ‘’the melody’’ and every successful show has one.

Google BooksCrafty TV Writing:
Thinking Inside the Box
By Alex Epstein
New York, NY: Owl Books (Henry Holt and Company, LLC)
2006
Pg. XIX:
You heard the old joke about the dumb actress in Hollywood — she slept with the writer!

Google BooksAuthorship in Film Adaptation
Edited by Jack Boozer
Austin, TX: University of Texas Press
2008
Pg. 70:
As the old joke about a Hollywood starlet so dumb she slept with the writer attests, screenwriters are widely perceived as the least powerful collaborators on movies.

Google BooksMrs. Nixon:
A Novelist Imagines a Life
By Ann Beattie
New York, NY: Scriber
2011
Pg. 121:
RN was also the scriptwriter (old joke in Hollywood: “She was so stupid, she slept with the writer”).